The disparity in the impact of COVID19 on minority populations in the United States has been well established in the available data on deaths, case counts, and adverse outcomes. However, critical metrics used by public health officials and epidemiologists, such as a time dependent viral reproductive number (
It is shown that for any positive integer
 NSFPAR ID:
 10422237
 Date Published:
 Journal Name:
 Discrete and Continuous Dynamical Systems  S
 Volume:
 15
 Issue:
 9
 ISSN:
 19371632
 Page Range / eLocation ID:
 2497
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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null (Ed.)
), can be hard to calculate from this data especially for individual populations. Furthermore, disparities in the availability of testing, record keeping infrastructure, or government funding in disadvantaged populations can produce incomplete data sets. In this work, we apply ensemble data assimilation techniques which optimally combine model and data to produce a more complete data set providing better estimates of the critical metrics used by public health officials and epidemiologists. We employ a multipopulation SEIR (Susceptible, Exposed, Infected and Recovered) model with a time dependent reproductive number and age stratified contact rate matrix for each population. We assimilate the daily death data for populations separated by ethnic/racial groupings using a technique called Ensemble Smoothing with Multiple Data Assimilation (ESMDA) to estimate model parameters and produce an\begin{document}$ R_t $\end{document} for the\begin{document}$R_t(n)$\end{document} population. We do this with three distinct approaches, (1) using the same contact matrices and prior\begin{document}$n^{th}$\end{document} for each population, (2) assigning contact matrices with increased contact rates for working age and older adults to populations experiencing disparity and (3) as in (2) but with a timecontinuous update to\begin{document}$R_t(n)$\end{document} . We make a study of 9 U.S. states and the District of Columbia providing a complete time series of the pandemic in each and, in some cases, identifying disparities not otherwise evident in the aggregate statistics.\begin{document}$R_t(n)$\end{document} 
In this paper, we propose a new class of operator factorization methods to discretize the integral fractional Laplacian
for\begin{document}$ ( \Delta)^\frac{{ \alpha}}{{2}} $\end{document} . One main advantage is that our method can easily increase numerical accuracy by using highdegree Lagrange basis functions, but remain its scheme structure and computer implementation unchanged. Moreover, it results in a symmetric (multilevel) Toeplitz differentiation matrix, enabling efficient computation via the fast Fourier transforms. If constant or linear basis functions are used, our method has an accuracy of\begin{document}$ \alpha \in (0, 2) $\end{document} , while\begin{document}$ {\mathcal O}(h^2) $\end{document} for quadratic basis functions with\begin{document}$ {\mathcal O}(h^4) $\end{document} a small mesh size. This accuracy can be achieved for any\begin{document}$ h $\end{document} and can be further increased if higherdegree basis functions are chosen. Numerical experiments are provided to approximate the fractional Laplacian and solve the fractional Poisson problems. It shows that if the solution of fractional Poisson problem satisfies\begin{document}$ \alpha \in (0, 2) $\end{document} for\begin{document}$ u \in C^{m, l}(\bar{ \Omega}) $\end{document} and\begin{document}$ m \in {\mathbb N} $\end{document} , our method has an accuracy of\begin{document}$ 0 < l < 1 $\end{document} for constant and linear basis functions, while\begin{document}$ {\mathcal O}(h^{\min\{m+l, \, 2\}}) $\end{document} for quadratic basis functions. Additionally, our method can be readily applied to approximate the generalized fractional Laplacians with symmetric kernel function, and numerical study on the tempered fractional Poisson problem demonstrates its efficiency.\begin{document}$ {\mathcal O}(h^{\min\{m+l, \, 4\}}) $\end{document} 
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